Laws of Motion of a Body on an Inclined Plane

What is an Inclined Plane?
An inclined plane is a sloping surface that makes an angle θ\thetaθ with the horizontal.
Example: A ramp, slide, or hill slope.

When a body is placed on an inclined plane, gravity, normal force, and (sometimes) friction act on it.

Forces Acting on the Body:

1. Gravitational Force (mg) – Acts vertically downward.
2. Normal Force (N) – Perpendicular to the plane.
3. Frictional Force (f) – Opposes motion (only if surface is rough).
4. Component of Gravity along the plane: mg sin⁡θ (pulls object down slope).
5. Component of Gravity perpendicular to plane: mg cos⁡θ (balanced by N).

Case 1: Smooth Inclined Plane (No Friction)

Acceleration of body:

Where:

• g= acceleration due to gravity
• θ= angle of slope

Case 2: Rough Inclined Plane (With Friction)

Acceleration of body:

Where:

• μ = coefficient of friction

Case 3: Body Moving Up the Inclined Plane

If a force FFF is applied upward:

Examples in Daily Life:

• A cart rolling down a ramp.
• A block sliding on a slope.
• Cyclists riding uphill/downhill.

Summary:

• On a slope, gravity is split into two components: mgsin⁡θ (down slope) and mgcos⁡θ (into slope).
• Friction reduces acceleration.
• Smoother slopes → faster motion, steeper slopes → higher acceleration.